Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Critical points of multivariables

  1. Mar 9, 2009 #1
    1. The problem statement, all variables and given/known data

    Find and classify all critical points of
    [tex]f(x,y) = x^3+2y^3-3x^2-3y^2-12y[/tex]

    2. Relevant equations

    3. The attempt at a solution

    So I've gotten to
    [tex]Fx = 3x^2 - 6x = 0[/tex]
    [tex]Fy = 6y^2 - 6y - 12 = 0[/tex]

    [tex]x=0, x=2, y=-1, y=2[/tex]

    Now I can't remember how to find the critical points from here.
    Any help is appreciated!
  2. jcsd
  3. Mar 9, 2009 #2


    User Avatar
    Science Advisor
    Homework Helper

    The critical points are where Fx=0 AND Fy=0. Why is that hard to remember? Offhand, I would say you have four of them.
  4. Mar 9, 2009 #3
    Oh yeah, thanks. And it's hard to remember because I'm still a student.
  5. Mar 10, 2009 #4


    Staff: Mentor

    It's not that much different from how it is with functions of one variable. If y = f(x), you look for values for which f'(x) = 0. With functions of two or more variables, you look for points for which all the partial derivatives are zero.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook